# Math Help - The Conical Pendulum

1. ## The Conical Pendulum

I'm stuck on this question:

A light inextensible string AB of length 3l has its ends fixed to two points A and B which are in a vertical line with A a distance l above B. A smooth ring of mass m is threaded on the string and is made to move in a horizontal circle centre B with a constant speed. Calculate the tension in he string and the speed of the ring.

When I tried to calculate th tension I found that I needed either the radius of the circle of the diatance from either A or B to the ring, which I don't have. Have I missed something in the question? Could someone help please?

2. Originally Posted by free_to_fly
I'm stuck on this question:

A light inextensible string AB of length 3l has its ends fixed to two points A and B which are in a vertical line with A a distance l above B. A smooth ring of mass m is threaded on the string and is made to move in a horizontal circle centre B with a constant speed. Calculate the tension in he string and the speed of the ring.

...
I've attached a sketch of the situation as I understand it.

If I'm right the string forms a right triangle where the sides x and y have the length 3l:

$x+y = 3l$ ....... [1]

$y^2 + l^2 = x^2$....... [2]

From [1] you get: $y = 3l - x$ . Substitute this term into [2]:

$(3l-x)^2 + l^2 = x^2~\iff~ 10l^2 = 6lx~\iff~ x=\frac53 \cdot l$

That means $y = \frac43 \cdot l$ which is the radius of the circle.